What is the LCD of 2 −1 and 3 +1 ?
1 answer:
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Answer:
The possible rational roots are
Step-by-step explanation:
We have been given the equation 3x^3+9x-6=0 and we have to list all possible rational roots by rational root theorem.
The factors of constant term are
The factors of leading coefficient are
From ration root theorem, the possible roots are the ratio of the factors of the constant term and the factors of the leading coefficient. We include both positive as well as negative, hence we must include plus minus.
Answer: 7 centimeters
Explanation:
Let triangle ABC and triangle CDE form a bow tie such that
- triangle ABC is smaller than triangle CDE
- Segment AC and segment CD are the north sides
- Segment BC and segment CE are the bottom sides
- AC = 6, CD = 42, CE = 36, BC = x
Since angle ACB and angle ECD are formed by intersecting segment AE and segment BD at point C, they are vertical angles. (See the attached picture) So, angle ACB and angle ECD are congruent.
Moreover when we form our bowtie, point A is in the north side and point E is in the bottom sides and this implies that angle BAC and angle CED are alternate interior angles as shown in the attached figure.
Since it is given in the problem that alternating interior angle are congruent, angle BAC and angle CED are congruent.
Now, we have the following pairs of angles in triangle ABC and triangle CDE that are congruent:
- angle BAC and angle CED
- angle ACB and angle ECD
By AA Similarity theorem, when we have two pairs of congruent angles for two triangles, then the two triangles are similar. So, triangle ABC and triangle CDE are similar.
In similar triangles, the sides that are opposite to the congruent angles are proportional to each other. So,
(1)
Since
, we can substitute these values to equation (1). So, equation (1) becomes
(2)
SInce we are solving for x, we can multiply both sides of equation (2) by the denominator at the left side which is 42 so that
x = 42(1/6)
x = 7 centimeters
Explanation:
Let triangle ABC and triangle CDE form a bow tie such that
- triangle ABC is smaller than triangle CDE
- Segment AC and segment CD are the north sides
- Segment BC and segment CE are the bottom sides
- AC = 6, CD = 42, CE = 36, BC = x
Since angle ACB and angle ECD are formed by intersecting segment AE and segment BD at point C, they are vertical angles. (See the attached picture) So, angle ACB and angle ECD are congruent.
Moreover when we form our bowtie, point A is in the north side and point E is in the bottom sides and this implies that angle BAC and angle CED are alternate interior angles as shown in the attached figure.
Since it is given in the problem that alternating interior angle are congruent, angle BAC and angle CED are congruent.
Now, we have the following pairs of angles in triangle ABC and triangle CDE that are congruent:
- angle BAC and angle CED
- angle ACB and angle ECD
By AA Similarity theorem, when we have two pairs of congruent angles for two triangles, then the two triangles are similar. So, triangle ABC and triangle CDE are similar.
In similar triangles, the sides that are opposite to the congruent angles are proportional to each other. So,
Since
SInce we are solving for x, we can multiply both sides of equation (2) by the denominator at the left side which is 42 so that
x = 42(1/6)
x = 7 centimeters